1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
astraxan [27]
3 years ago
6

How do you find the x intercepts of 3x^(5/3) - 4x^(7/3)

Mathematics
2 answers:
kaheart [24]3 years ago
7 0
Set the whole expression = to 0 and solve for x.

3x^(5/3) - 4x^(7/3) = 0.  Factor out x^(5/3):     x^(5/3) [3 - 4x^(2/3)] = 0

Then either x^(5/3) = 0, or 3 - 4x^(2/3) = 0.

In the latter case, 4x^(2/3) = 3. 

To solve this:  mult. both sides by x^(-2/3).  Then we have

4x^(2/3)x^(-2/3) = 3x^(-2/3),            or 4 = 3x^(-2/3).  It'd be easier to work with this if we rewrote it as

4           3
---  = --------------------
1            x^(+2/3)

Then 

4
---  = x^(-2/3).  Then, x^(2/3) = (3/4), and x = (3/4)^(3/2).  According to my     3                      calculator, that comes out to x = 0.65 (approx.)

Check this result!  subst. 0.65 for x in the given equation.  Is the equation then true?

My method here was a bit roundabout, and longer than it should have been.  Can you think of a more elegant (and shorter) solution?
Varvara68 [4.7K]3 years ago
7 0
To the risk of sounding redundant, as Altavistard already pointed out above

\bf 3x^{\frac{5}{3}}-4x^{\frac{7}{3}}=0\implies \stackrel{common~factor}{x^{\frac{5}{3}}}(3-4x^{\frac{2}{3}})=0\\\\
-------------------------------\\\\
x^{\frac{5}{3}}=0\implies \boxed{x=0}\\\\
-------------------------------\\\\
3-4x^{\frac{2}{3}}=0\implies 3=4x^{\frac{2}{3}}\implies (3)^3=\left(4x^{\frac{2}{3}}\right)^3
\\\\\\
27=64x^2\implies \cfrac{27}{64}=x^2\implies \sqrt{\cfrac{27}{64}}=x\implies \boxed{\cfrac{3\sqrt{3}}{4\sqrt{4}}=x}
\\\\\\
0.64951905283832898507\approx x
You might be interested in
17. Factor x ^ 3 + 5x ^ 2 - 9x - 45 . A. (x - 5)(x ^ 2 + 9) b . (x - 5)(x - 3) * (x + 3) Factor By Groupin (x + 5)(x - 3) * (x +
jok3333 [9.3K]

Answer:

b

Step-by-step explanation:

Given

x³ + 5x² - 9x - 45 ( factor the first/second and third/fourth terms )

= x²(x + 5) - 9(x + 5) ← factor out (x + 5) from each term

= (x + 5)(x² - 9) ← factor as a difference of squares

= (x + 5)(x - 3)(x + 3)

3 0
3 years ago
Which of the following numbers belong to the set of complex numbers AND The set of imaginary numbers? Select all that apply.
Schach [20]
<span>To be both complex and imaginary, the answer would have to include "i" as well as have the form "a + bi". The first example, 3i - 5, fits. This would look to be the only example that does fit. The negative square root of 14 would be imaginary, but not complex.</span>
7 0
3 years ago
Rewrite each sum as a product of the Gcf of the addends and another number. 15+45
morpeh [17]
15 + 45

GCF = 15

15/15 = 1
45/15 = 3

(15 * 1) + (15 * 3) = 
15(1 + 3) <===
8 0
3 years ago
A line passes through the points (2,21) and (8,27). Write a linear function rule in terms of x and y for
tatiyna
We have two points so we can find the gradient using y1-y2/x1-x2
gradient = 21-27/2-8
= 1
we know the form for any linear equation is y = mx + c
we have m and a point so we can substitute in point (2,21) to find c
21 = 1 x 2 + c
c = 19
therefore, the equation is y = x + 19
6 0
2 years ago
Read 2 more answers
In science class Abigail Broadway 0.88 kilogram what is the value of the digit in the tenths place
zaharov [31]
0.88......ones (decimal), tenths, hundredths
so 8 is in the tenths place....8/10
7 0
3 years ago
Other questions:
  • a bank advertises a 2/1 ARM at 5.15% with a 2/6 cap. what is the maximum interest rate that can be charged during the fifth year
    10·1 answer
  • Please help me in the question above? Please!!
    10·1 answer
  • Sonya wants to put a ribbon border along the edge of her round tablecloth. The ribbon is sold in one-inch increments. If the dia
    10·1 answer
  • 1. 7:__= 63: 36 and 2. __: 24 = 4: 3
    5·1 answer
  • reduce the following fractions to their lowest terms: a. 6/8. b. 8/12c. 15/20 d. 9/18 e. 24/30 f. 25/40​
    5·1 answer
  • The following question is located in the attachment.
    11·2 answers
  • What is the price of a $13 ticket with a 8% sales tax?
    10·2 answers
  • Brian invests £13400 into his bank account.
    13·1 answer
  • Hank's Hardware purchased a barbecue grill for $350.36 and marked it up 185%. During a sale, the store marked it down 20%. What
    12·1 answer
  • Is the graph increasing, decreasing, or constant?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!